Pure state Ne*(*)[|J, M⪢]-preparation in a magnetic field: Polarization effects in ionizing collisions

Chemical Physics 147 ( 1990) 447-465 North-Holland

Pure state Ne*(*) [ 1J, 44) ]-preparation in a magnetic field: polarization effects in ionizing collisions J.P.J. Driessen *, H.J.L. Megens, M.J. Zonneveld, H.C.W. Beijerinck and B.J. Verhaar

H.A.J. Senhorst,

Physics Department, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven. The Netherlands

Received 2 May 1990

A compact device (length 175 mm) has been built for the energy resolved detection of low energy (1-5 eV) Penning electrons with a 271solid angle collection efficiency, based on the principle of adiabatic parallelisation of electron motion in a diverging magnetic field. A retarding field analysis is then used as a high pass tilter to discriminate between Penning electrons released in collisions of rare gas atoms in metastable and shortlived, laser excited states. The overall detection efficiency is 0.13. The Zeemansplitting of the atomic levels in the scattering center (maximum B=222 G) allows the preparation of single magnetic substates IJ, M),. By rotating the detector in the collision plane, well defined IJ, M), states can be produced with respect to the relative velocity g, the quantization axis relevant for the collisions. The system has been tested by measuring the collision energy dependenceof polarized-atomcrosssections’Q MIfor the Ne*[“P2]-Arand Ne**[3D,]-Arsystems. For the Ne* [ 3P2] metastable atoms we find zQ”/ *Q*= I.55 f 0.06 and 1.05 k 0.06 in the thermal and superthermal energy range, respectively, which should be compared to I .30 of Bregel et al. at thermal energies. For the Ne** [ 'D3 ] state we find ‘Q’.‘/ ‘Qze3= 1.65 k 0.06 and I .OOf 0.10 for the same energy ranges.

1. Introduction

Inelastic collisions involving atoms in electronically laser excited states have proven to reveal interesting features of the potential surfaces and the collision dynamics. The excited atoms are prepared in a well defined asymptotic polarized state, determined by the laser polarization. Strong effects of the orientation on cross section magnitude have been observed [ 1- 13 1. The link between the observed polarization effects and the angle dependent potential curves is governed by the collision dynamics. Our own work is devoted mainly to inelastic collisions with metastable Ne*[ (2~)~(3s); ‘PO, ‘P,]-atoms [ 14, 151 or short-lived laser excited Ne** [ (2p)‘(3p)]=Ne**[ak] states [9-131, with k running from 1 to 10 with decreasing energy, according to the Paschen numbering. As a collision partner we use rare gas atoms. For these systems potential surface information is available, enabling us to obtain detailed insight into the mechanism governing the collision pro’ Presentaddress:JILA,Boulder,CO 80309-0440,USA. 0301-0104/90/$03.50

cess. In many cases, however, no accurate information is available on the coupling potentials for the systems under consideration. In a collision experiment the excited atom can be prepared in an initial state 1J, M), in a space-fixed frame, with the relative velocity g as the quantization-axis. The inelastic process, however, is described in a body-fixed frame with quantum numbers IJ, SZ)R for the total electronic angular momentum J and its orientation L2with respect to the internuclear axis R.The Q-dependent probabilities of these inelastic processes are the main objective of our research. The collision dynamics describes the spatial evolution of the asymptotic initial state (J, M) to the local molecular states (J, 8) along the particle trajectory. This L&scrambling has a large influence on the polarized-atom cross sections and thus on the observed polarization effects. In a semiclassical analysis [ 131 the concept of “locking”, i.e. the coupling of J to the internuclear axis, has proven essential to explain the strong energy dependence of the observed polarization effect in ionizing collisions of Ne** [(Ye,J= 3 ] -Ar.

0 1990 - Elsevier Science Publishers B.V. (North-Holland)

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J.P.J. Driessen et al. /Purestate Neg. Ne**preparation

Most detailed information is obtained if a pure magnetic substate 1J, M), is excited. In many cases, however, both atomic states involved in the excitation process are degenerate (M= -J, .... + J) and a broad M-distribution of initial states 1J, M), is excited. In an external magnetic field B this degeneracy is removed and pure substates 1J, M), can be excited. In order to measure the polarized-atom cross sections “Q’“’ for an asymptotically pure magnetic substate )J, M), separately, it is necessary to align the magnetic field with respect to the relative velocity VW). This work focuses on ionizing collisions with neon atoms excited in the two-level system colliding with Ar Ne**[+, 5=3] +Ar 1

hv

--c

Ne’[‘P2] +Ar 77

Ne+ Ar+ +e-(e,=e0+hY=2.7eV) (NeAr)+ +e-(e,ceO+hY*2.9eV) Ne+Ar+ +e-(eox0.9eV) (NeAr)+ +e-(eox 1.1 eV) .

In the absence of an external magnetic field, a stationary polarized M-distribution of both levels is excited, due to the repeated excitation. In this configuration it is not possible to excite pure substates with respect to the relative velocity g, resulting in interdependent values of the polarized-atom cross sections. Hotop et al. [ 161 and Bussert et al. [ 51 have performed PIES-experiments for this collision system, resulting in fine-structure resolved cross sections for the 2P,,Z- and 2P3,z-states of the Ar+-ion. Bussert et al. [51 also measured the polarization effect in the ionization cross section. In our crossed beam experiment this polarization effect has been confirmed. Using time-of-flight techniques we have observed a strong energy dependence of the polarization effect in a broad energy range (0.05&E 6 5 eV). So far, we studied the ionization process in our experimental setup by collecting all the produced ions, Ar+ and (NeAr) +, in an electric field. Because we are not able to discern directly between the two processes of eq. ( 1 ), we have to apply a laser-modulation technique resulting in the difference cross section

AQ(E) = 3Q(E) - ‘Q(E) >

(2)

with superscripts 2 and 3 referring to the J quantum number of the lower and upper state of the neon twolevel system, respectively. Because both levels become polarized, the interpretation of the difference cross section AQ( E) in polarized-atom cross sections 2QlMl (E) and 3Q t”I (E) is complicated, as has been described by Driessen et al. [ 13 1. It is our aim to improve the experimental setup, so as to separate the two collision processes of eq. ( 1). This requirement can only be met if we detect the Penning electrons energy-resolved instead of detecting the ions. In order to get comparable signals for both detection-techniques, we want to collect all the emitted electrons in the scattering process. Kruit and Read [ 171 have demonstrated that it is possible to collect the electrons emitted over a 2x:solid angle in a magnetic field, without disturbing the electron energy. The random emitted electrons are aligned along a decreasing magnetic field. Energy selection of the Penning electrons of eq. ( 1) is now possible, because the probability distributions P( u, )dv, of the longitudinal component become separated. The fast Penning electrons of eq. ( la) can be detected separately, with a retarding field blocking the slow electrons of eq. ( 1b ) . We have built an electron detector, with a 2a solid angle collection of the emitted electrons. Because an external magnetic field is applied in the scattering center, we are able to excite pure magnetic substates IJ, M).. To determine the polarized-atom cross sections JQ’“l (E) as accurately as possible, we have to align the magnetic field along the relative velocity. With time-of-flight analysis in our crossed beam apparatus, the velocityg has no unique direction. Therefore, we have made the detector rotatable in the collision plane, enabling us to prepare pure magnetic substates IJ, M), The plan of this paper is as follows. In section 2 the different aspects of the crossed beam apparatus will be discussed. The principle of operation of the electron detector is outlined as well as the conditions that must be satisfied for an ideal behaviour. The preparation of pure Zeeman-states in a magnetic field B with a detuned laser beam is described in section 3 to complete the picture of the experimental setup. In section 4 we will present measurements of the polarized-atom cross sections 2Q’M’(E) for the Ne* [ 3P2, Ml-Ar system. By depleting a single magnetic substate IJ, M), of the metastable Ne* [ 3P2]-

J.P.J. Driessenet al. /Purestate Ne*. Ne**preparation

state, this polarization effect can be determined with a laser-modulation technique. In section 5 the experimental data for the polarized-atom cross section 3QtM’(E) for the Ne** [ a9; J= 3, Ml-Ar system are given. In section 6 we discuss the experimental results and compare them with theoretical predictions.

2.1. Crossed beam apparatus The Penning ionization processes of eq. ( 1) are studied in a crossed beam setup, which has been described extensively by Verheijen et al. [ 14 1, van den Berg et al. [ 15 ] and Driessen et al. [ 13 1. A schematic view of the crossed beam experiment is given in fig. 1. The primary beam consisting of metastable Ne* [3P,-,,3P,]-atoms crosses a secondary beam, with a well defined and narrow beam-profile. For the production of metastable Ne*-atoms two different discharge beam sources are available: a hollow cathode arc discharge (HCA) for the superthermal energy range 0.5 G E( eV ) 4 5 and a discharge excited supersonic expansion (TMS) for the thermal energy range 0.05 i E( eV ) Q 0.2. Velocity analysis of the primary beam is performed using the time-of-flight technique, resulting in a well known relative velocity g. The metastable Ne*-atoms are detected by Auger emission from a stainless steel surface in combination with an electron multiplier. In the former setup we detected the ions, which were imaged onto a spir-

Fig. I. Schematic view of the crossed beam experiment: ( 1) primary beam; (2) secondary beam; (3) tim-f-fliit chopper disc; (4 ) scattering center; ( 5 ) metastable-atom detector, (6 ) beamdefining collimators; (7) laser beam directed perpendicular to the collision plane.

449

altron detector in an electric field. A 4x: solid angle collection of the ions was achieved. In a new setup we plan to detect the Penning electrons with energy analysis to discern between the two ionization processes of eq. ( 1) . By measuring with time-of-flight analysis the countrates for metastable-atom detection, Sm( fk), and final-state detection, Sian( tk) or Serec(f,J , we are able to determine the energy resolved ionization cross section according to Q(E)=(nlgk/vk)-‘~_

9-y tk) q” Sm( tk) 11’0”

or Q(E)=(nlg,lv~)-l$$f-&

(3)

with ( nlg,Jvk) the effective density-length product of the secondary beam, as seen by the primary Ne*beam. The efficiencies for detection of metastable atoms, ions and electrons are indicated by p, r,@”and flee, respectively. The density-length product (nl) of the secondary beam has been calibrated by Verheijen et al. [ 18 1. 2.2. Parallelisation mechanism If a laser beam is directed at the scattering center to excite the neon two-level system, Penning electrons are emitted in the ionization process which differ x 1.8 eV in kinetic energy (eq. ( 1) ). These electrons can be analyzed in a retarding field. In order to obtain an appreciable countrate for electron detection, the solid-angle acceptance must be large. Collection of the electron over large solid angles is difftcult to achieve without disturbing the energy resolution. This problem has been overcome using the properties of an inhomogeneous magnetic field, as described earlier by Hsu et al. [ 19 ] and Kruit et al. [ 17 1. The Lorentz force evxBcauses each emitted electron to spiral around a magnetic field line. When going from high-field to low-field regions, the Lorentz-force has a component along the central axis of the helical motion. This causes the longitudinal velocity component v,,to increase and, since the total velocity v is constant, the transverse component vI to decrease giving the effect of parallelisation. This exchange of energy is caused by the adiabatic invariance of the

J.P.J. Driessen et al. /Pure state Ne? Ne’*preparation

450

magnetic moment, which means that the magnetic flux linked by the electron orbit is a constant of the motion. The field variation experienced by the electron in the course of one revolution must be negligible with respect to the total field to satisfy the condition of adiabatic behaviour [ 201. In an inverse sense, this principle has been used as a “magnetic mirror”. In an increasing magnetic field the transverse velocity vL is increased at the expense of v,,, resulting in possible reflection of the trajectories. In fig. 2 we illustrate the essence of the parallelisation mechanism as discussed previously by Kruit et al. [ 171. An electron with energy CO =

+m,v2=

tmd

+

(4)

tm,vi,

The angle &of the helical motion in the low field ( Bf) is thus given by sin & sin==

0 Br

l/2

Cl.

(7)

The transverse velocity component vI is therefore reduced, with a corresponding increase of the longitudinal velocity component Vil,i = v cos 0, to v,,,~=v[

I-

(Bf/Bi)

sin2@]“’ .

(8)

Electrons emitted isotropically with kinetic energy eo, will obtain a distribution of longitudinal energy Ell,f = 4me v& according to P(E,,,f) d&r

initially emitted in a high-field region (Bi) at an angle 0, to the zdirection and velocity v, moves on a helical trajectory in the magnetic field with a cyclotron radius

(5) with vI = v sin 0,. The particle moves adiabatically into a weaker magnetic field (&< Bi). From the adiabatic invariance of the magnetic moment we have

It is apparent from this distribution that the Penning electrons of eq. ( 1) can be energy analyzed by choosing a suitable small value for Bf/Bi. 2.3. Magnet design

2 nr&

Ba 5

= constant .

(6)

---

Some practical conditions must be fulfilled to apply a magnetic field in the scattering center of our

”

“1.i Oil

p “Il,i

Bf

\

Fig. 2. Schematic diagram of the helical trajectory of an electron moving in a magnetic field, which decreases adiabatically from Bi to &. The angles Bof the helical motion with respect to the z-axis are indicated as well.

J.P.J. D&men et al. /Pure state Ne*, Ne** preparation

crossed beam apparatus. First, we want to excite pure magnetic substates IJ, M) B (section 1). The degeneracy of the Ne *(*‘-states is removed through the Zeeman-splitting, which must be large compared to the line-width of the saturated optical transition. We find that the field value must satisfy B& 175 G with a homogeneity of better than 3% in order to be able to excite the Ne*(*) [ IJ, M),]-states with a purity of 295% (section 3.1). Second, we demand that the atomic beams may not be disturbed by the magnets, to avoid possible emission of secondary electrons and to prevent a build-up of residual gas pressure. This implies that the collision plane must be kept free in the magnet design. Moreover, we need an opening through which the laser beam can be directed at the scattering center. Thirdly, the field maximum must coincide with the interaction region to prevent possible reflection of electron trajectories on either side. This implies that the divergence of the magnetic field in the scattering center will be minimal, ensuring an optimal homogeneity. Furthermore, the magnetic field must decrease adiabatically to parallel& the electron trajectories. Another requirement is obvious: when the Penning electrons have been energy analyzed in a retarding field, the magnetic field may not influence the electron detection. Finally, the dimensions of the crossed beam apparatus limit the size

451

of the new electron detection device, which must be rotatable in the collision plane in order to prepare pure Zeeman-states with respect to the relative velocity g. The parallelisation, energy analysis and detection of the emitted electrons must occur within a distance of 175 mm from the scattering center. For practical reasons we have chosen to use permanent magnets [ 2 11, made of Ferroxdure 400 with an internal magnetization of 4000 G. In a computer simulation, various magnet designs have been tested. The decreasing magnetic field is best reproduced with a cone-shaped magnet. This conical shape is approximated in practice by six ring magnets of increasing diameter and simultaneous decreasing thickness. To keep the collision plane undisturbed, we have removed 40”~segments on opposite sides of the ring magnets. This leaves us with two cone-shaped segments which are to be placed symmetrically with respect to the collision plane. Two openings are made in the cone-shaped magnets in order to direct the laser beam at the interaction region, perpendicular to the collision plane. A schematic view of the final magnet design is presented in fig. 3. In a computer simulation we have calculated the magnetic field configuration of the final magnet design, including the effect of the two laser beam openings. The calculated field lines are depicted in fig. 3.

x (mm) 40

i

I

0

30

I I

10

I

I

,

20

30

40

I

50

zlmml

Fig. 3. Design of the magnet section: ( 1) permanent ring magnets; (2) laser beam axis= rotation axis; ( 3) opening for laser beam; (4) computed pattern of the magnetic field.

J.P.J. Driessen et al. /Purestate Ne*, Ne** preparation

452

2.4. Energy-analysis and electron detection

0

10

20

30

40

z(mm1

Fig. 4. Calculated value of the magnetic field along three field lines as a function of z: ( I ) field line on the axis (straight line); (2) field line in a plane perpendicular to the collision plane; 4 mm from the axis in the scatteringcenter (dashed line); (3) field line in the collision plane; 4 mm from the axis in the scattering center (dotted line).

The maximum of the magnetic field is equal to B=209 G and is located at position z=9 mm. The field decreases adiabatically with z in either direction. In fig. 4 the absolute B-value is shown for three field lines: one on the axis, the other two located at a distance of 4 mm from the interaction region. At a distance AZ= 32 mm from the scattering center, the magnetic field has decreased with a factor of 5. According to eq. (8), energy analysis of the Penning electrons emitted in the ionization process is now possible. At this position the retarding field will be located. Experimentally, we have verified the magnetic field configuration using a threedimensional Hall-probe. The absolute value is 7% larger than calculated. The general shape of the calculated field pattern is reproduced fairly accurately. The maximum is located at 2~8.5 mm with 8~224 G. The field homogeneity is found to be better than 2% over the volume of the scattering center (2x2~2 mm’). In the region behind the retarding field (z& 45 mm), the field is less than 15 G. Electron detection with a channeltron detector in this region is therefore not disturbed by the magnetic field. With this magnet design, it is thus possible to parallelise and analyse the Penning electrons emitted in the ionization processes of eq. ( 1).

The emitted electrons will spiral around the field lines with a cyclotron radius rEyC(es. (5) ). For the fast electrons of eq. ( la) we find r,,90.28 mm in the scattering center. In combination with the dimension of the interaction region (2 X 2 X 2 mm3), we find that the electron distribution is magnified to a diameter of 7 mm at the retarding field position. Therefore, the retarding field must be of a larger size. After the electrons have been energy analyzed they have to be imaged onto a channeltron detector. For this purpose we use a configuration of two electrostatic lenses in combination with an electron mirror, which have been schematically drawn in fig. 5. If a magnetic substate Ne* [ ‘PZ, M] is depleted in the interaction region to determine the polarized-atom cross section 2Q ~1 (E), W-photons are produced in the resonant decay. Because the channeltron detector is sensitive to UV-photons, the scattering center must be out of view of the electron detector. Therefore, an electron mirror is used. The transparency of the grids used for energy analysis and electron imaging must be as large as possible, to obtain a maximum collection efficiency for the emitted electrons. The gratings are made by winding tungsten-wire with a diameter of 6 pm onto a fmmework, giving parallel lines at relative distances of 1 mm with an overall transparency of 99.4%. For the retarding field three grids are used with a relative spacing of 1 mm. The first grid is used to screen the scattering center from the retarding field. The selection voltage is applied to the other two grids. The retarding field of this configuration is simulated on resistance paper. Due to the open structure of the selection grids, the effective blocking voltage is approximately 40% lower than the applied voltage. Over 90% of the grid area the effective voltage is constant with a sharp increase close to the tungsten-wires. Because we need a crude energy analysis to discern between electrons of ~~~0.9 eV and e, ~2.7 eV, this configuration is quite suited for its purpose. When the electrons have passed the energy selector, they are accelerated to minimize the influence of the residual magnetic field. The first electron lens focuses the electrons onto the electron mirror, where they are deflected in an upward direction+ With a second lens the electrons are imaged onto the channeltron detec-

J.P.J. Driessen et al. /Pure state Ne*, Ne**preparation

1000 I/s

453

511s I

I

-50

I

I

I,

I

I

I,,

,

0

50

,

,

, 100

,

,

1,,

150

ztmml side view

Fig 5. Schematic view of the setup for energy-analysis and detection ofthe emitted Penning electrons: ( I ) screening grid ( U=O V); (2) two selection grids for the energy analysis; (3) accelerating grid, (4) electron lens; (5) screening grid; (6) the electron mirror, (7) screening grid, (8) electron lens; (9) grid to accelerate the electrons to Ed=200 eV, for a optimum detection effkiency at ( 10) the channeltron detector; ( 11) the ring magnets. The grids and magnets are mounted onto ( 12) an aluminum construction. The distance scale has also been indicated together with a schematic view of the secondary beam setup.

tor. From scattering center to detector, the electrons pass nine grids. The total transparency T= 0.9949=0.947 is very high due to the high transpar-

ency of the separate grids. In fig. 6 we have schematically drawn the configuration of the electron energy analyzer with respect to

top view

g>HCA

B -range

Fig. 6. Top view of the collision plane. The angular ranges of the magnetic field B and of the relative velocity g am depicted, which are characterized by the lab-angles 6, and 8, Perfect alignment of B and g is not possible for all collision energies. With respect to the average relative velocities (g>and (g)ucAthe minimum angles j?= L (B, g)=&,-0, are given by: /Yzms= 10’ and /?Ey =27”.

J. P.J. Driessen et al. /Pure state Ne? Ne* preparation

454

the collision plane. The total dimension of the apparatus in this plane is 170 mm. The device is rotatable in the collision plane with respect to the scattering center, over lab-angles 35” < 0, ( 145”. The laser beam is directed perpendicular to the collision plane, through a hollow tube serving as the rotation axis. The direction of the relative velocitygdepends on the primary beam velocity. For the two primary beam sources we have 5 ’ Q 0, d 40”. Perfect alignment of B and g is therefore not possible at all energies. The ave:age relative velocities (gjTMs and (g)HCA for both metastable sources have been indicated. The minimum angles /I= L (B, g) with respect to these average velocities are pm,” = 10 ’ and EEA = 27 ‘.

3. Optical pumping in a magnetic field 3.1. Zeeman-splitting In a magnetic field B the degeneracy of the Ne*(*) [ IJ, M) ]-substates is removed by the Zeeman effect [ 22 1. The energy-splitting can be treated as a small perturbation with respect to the atomic energies E,, resulting in 2J+ 1 levels with energy E ,w=&-MwtsB,

(10)

with M= -J, -J+ 1, .... + J, pe the Bohr magneton and gL the so-called Land6 factor of the energy level considered. In table 1 the Land6 factors of the Ne*(*)-levels are given as determined by Pinnington Table 1 The LandCfacton for the Ne*‘*)-states as determined by Pinnington [ 231. The number in parentheses is the error in the last digit given

‘PI ‘PO 3PI 3P*

1.037(2) 0.0 1.464(4) 1.501(4)

0.0

1.340(3) 0.0 1.298(4) 0.994(4) 1.232(2) 0.678 ( I ) 1.137(l) 1.335(2) 1.989(3)

[231. The optical transition-frequencies are thus shifted with respect to the undisturbed excitation frequency v. by an amount Av~+~~ given by Av.+.u~ = v=

kL,k~k-&,iM

(vo+Av~+~lr)

1y

,

9

(11)

for a transition Ne* [ ‘P,; Mi] +Ne** [ LYE;Jk, Mk]. Because the g,-factors of the upper and lower level are different, none of the separate transitions corresponds to exactly the same energy jump. This is called the anomalous Zeeman effect. For small splittings of the levels with respect to the distance between the unperturbed levels the coupling schemes of the Ne*(*)atom are not influenced. This condition is satisfied in our magnetic field. With a field of B= 224 G in the scattering center, the maximum Zeeman-shift is Av,,, = 750 MHz for the transition

+Ne**[c+;J,=l,M=l].

(12)

In order to excite pure magnetic substates Ne* (* ) [ 1J, M) #], the splitting of the optical transition frequencies must be large compared with the linewidth of the transition. We have performed a computer simulation of the excitation process in the magnetic field to calculate the minimum Zeemansplitting and the maximum broadening of the transition lines. This broadening is a result of the inhomogeneity of the field over the interaction region and the divergence of the primary Ne*-beam. The calculation shows that the magnetic field value must be larger than 175 G and that the homogeneity of the magnetic field over the interaction region must be better than 3%. These requirements are met in our magnet design (section 2.4). For optical pumping in the magnetic field, the laser must be stabilized on the Zeeman-shifted transitionfrequency. The principle of absolute frequency stabilization of the single-mode cw dye-laser is described by Verheijen et al. [ 241. First, the laser-frequency is coupled to the resonance frequency of a Fabry-Perot interferometer by control of the endmirror and tine-tuning etalon of the dye-laser. Because the interferometer is thermally stabilized (AT= 0.01 K), the drift of the laser frequency is less

J.P.J. Driessen et al. /Purestate Ne*, Ne**preparation

than 0.5 MHz/min. The second loop of the process stabilizes the laser on the optical transition by measuring the fluorescence signal of an atomic beam crossing the laser beam at right angles. This stabilization on the natural transition-frequency Y, is performed intermittently at time intervals ranging from lot0 100s. Stabilization of the Zeeman-shifted transition-frequency is now achieved by detuning the resonance frequency of the interferometer piezo-electrically, with a sensitivity of 36.0 k 0.1 MHz/V. The voltage is varied in steps of AUx 13.45 + 0.05 mV, which corresponds to a frequency detuning in steps of Au= 0.484 + 0.002 MHz, which is small compared to the natural linewidth of the optical transition (AVhuhm = 10 MHz ) . For the maximum Zeeman-shift (Au= 750 MHz) a voltage of 20.8 k 0.1 V is needed. The performance of this frequency detuning and stabilization is discussed in the next section. 3.2. Experimental results Before we can excite pure magnetic substates, we have to cross the laser beam at right angles with the primary Ne*-beam. Perpendicular alignment can be achieved by optimizing the Ne*-depletion [ 251, resulting from optical excitation to a Ne** [ ak; J# 3]level with the laser stabilized at the natural transition-frequency vo. The laser-induced Ne*-modulation is determined experimentally with the metastable-atom detector in the crossed beam apparatus (fig. 1). In this procedure we have to be sure that the Zeeman-shifted frequencies are not compensated by a Doppler-shift. The minimum number of Zeeman lines is three for a J=O+J= 1 transition, as encountered for the Ne* [ 3Po] -+Ne** [ CQ, Jk = 1 ] transition. By choosing a linear laser polarization with electric field vector E parallel to the magnetic field B, we know that only U=O-transitions can be excited. In this configuration we only have a single Zeeman line that is excited at the undisturbed transition frequency vo. We can now use the normal procedure to achieve perpendicular alignment of laser and atomic Ne*-beam [ 25 1. The laser beam axis is fixed in space at two points, using a pinhole at one position and a light-sensitive quadrant-diode at the other position. The performance of the experimental setup to pre-

455

pare pure magnetic substates is now tested, by measuring the Ne*depletion as a function of the frequency detuning. For the optical pumping of the Ne* [ 3Pz; Ml-states, the laser is tuned to the optical transition Ne*[‘Pz, J=2,A4i]+hvMi_Mk -+Ne**[cu,; J8 =2, iI&] .

(13)

For the two independent laser configurations El/B and El. B, we have measured the attenuation of the primary Ne*-beam. The photons can be represented as IS= 1, M=O)-states with respect to the optical quantization-axis E. Thus, in the El1B-configuration only A&f= O-transitions with respect to the magnetic field B are excited. The M=OAM=O-transition, however, is forbidden as determined by the ClebschGordan coeficients. In the other situation, with El. B, the photons are described as {fi[ IS= 1, M= Therefore, only I)= f )S= 1 ,M= - 1 ),I-states. &+4= k l-transitions will be excited with respect to the magnetic field. The maximum expected attenuation of the Ne*beam is 15%, which is determined by the natural abundance of the neon isotopes (90.9% 2eNe; 9.1% “Ne) and a statistical distribution over the magnetic substates of the metastable Ne* [ ‘PO, ‘P,]-atoms. In the resonant decay a small fraction of the pumped Ne*-atoms ends up in the neighbouring magnetic substates, leading to pumping efficiencies smaller than 15% as will be shown in table 2. The Zeeman splitting of the transition 3Pz~~8 is schematically drawn in fig. 7, together with the splitting of the neon two-level system of eq. ( I ). The experimental results of the Ne*-depletion are presented in fig. 8. The independence of the two laser configurations is clearly demonstrated: no hM= O-transitions are excited for the perpendicular alignment (El B) and no m= f 1-transitions are observed for the aligned configuration (El1B). In a least-squares analysis of the data we have determined the Ne*depletion for each Zeeman line and the linewidth of its Lorentz profile. The results of this analysis are given in table 2. The resulting curve has been included in rig. 8. We observe that the broadening of the lines in the Zeeman spectrum is indeed negligible compared to the frequency spacing of the twelve separate spectroscopic lines, indicating that the Zeeman transi-

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456

Table 2 In a least-squares analysis of the Zeeman spectra of figs. I?and 9, the Ne*depletion and the linewidth of each Zeeman line have been obtained. From the peak positions we have determined the Land6 factors of the three levels involved (tig. 7). According to eq. ( I 1) we find a magnetic tield of 8=222 f 1 G. The number in parentheses is the error in the last digit given Mi-+Mc

Transition

Depletion (96)

Linewidth (MHz)

1, 12 2,lI 3, JO 4, 9 5, 8 6, 7

2/6 3/6 316 2/6 116 416

12.0(4) 12.5(4) 12.8(3) 11.7(3) I1.3(3) 14.7(2)

26.8+ 31.2f 30.2 + 27.1? 31.2f 56.9 f

S’, 11’

I

13.5(7)

18.0? 1.4

Ne*(*)-state

1.4 1.4 1.2 1.2 1.4

1.4

Land6 factor this work

Pinnington 1231

1.499(2)

I.501 (4) 1.137(l) 1.335(2)

1.136(2) 1.338(l)

11’ 6’

II

II

I1

t

1

I

1

II

I1

I

Fig. 7. The Zeeman-splitting AE(a,) = 1.89 MHz/G.

of the ‘P2~as

and the ‘P *+vY~transitions. AE(“P2)=2.10

tions can be excited independently. Thus, we can perform experiments of pure Ne* [ 3P2; IJ= 2, M),]states colliding with Ar using the laser-modulation technique. The results of this collision process are presented in section 4. As stated earlier, we aim to study the polarization effect in ionizing collisions of Ne** [a,; J= 3, Ml-atoms as well. In the magnetic field B the degeneracy

MHz/G, AE(as)=1.59

MHz/G and

of upper and lower level is removed. Only two LW= + l-transitions form true two-level systems, namely Ne*[3Pz;Mi=+2]+hV~i_M* +Ne**[Cy,;J=3,&=

+3].

(141

In these two-level systems significant electron count-

J.P.J. Driessen et al. /Pure state Ne? Ne**preparation

tt -5 -800

,

I

-400

tt 6

5,

,

0

AVM, _Mk 20 3

I

I

I

15-

-5900

I

7 ,8

, 400

I 800

Av,,i_Mk

(MHz1 I

I

I

t

2

b

r t

3 4 -400 Av

IMHzl

Fig. 9. The Ne*decrease resulting from optical deflection of the two-level system (eq. ( 14) ) in the magnetic field as a function of the laser frequency, measured at I= 10.0 mW. The laser polarization is aligned perpendicular to the magnetic field (AM= k 1) . The numbers indicate the transitions in fig. 7.

ElB

f

457

J coo

Fig. 8. The Ne*depletion in the magnetic field at I= 1.0 mW as a function of the laser frequency, with the laser tuned to the ‘P2~cus transition (es. (13)). (a) Laser polarization along the magnetic field (El[B, AM=O); (b) laser polarization perpendicular to the magnetic field (EIB; AM= f 1). The numbers indicate the transitions in fig. 7.

rates can be obtained in the ionization experiment for the excited upper state, because the population of both levels is comparable in the laser beam profile. The excitation of this transition cannot be tested through Ne*-depletion. However, due to the repeated excitation in the two-level system, the metastable Ne*-atoms are deflected. For sufficiently high laser intensities the deflection becomes so large that the metastable atoms hit the atomic beam collimator and do not reach the metastable-atom detector (fig. 1). For all other transitions a stationary population distribution cannot be achieved and the resulting electron countrates are too small to perform collision experiments. Experimental results for the decrease of the Ne*-

signal are shown in fig. 9. A Lorentz profile through the data, shown in fig. 9 as well, gives a poor representation of the results. The reason for this is the large number of excitations (N> 30) required to deflect a Ne*-atom out of the solid angle seen by the detector. For a detuned laser frequency the number of excitations is not sufftcient to deflect the Ne*-atoms. In the Ne*-beam a small detuning can compensate the Dop pler-shift of diverging Ne*-atoms and deflect them info the solid-angle acceptance of the Ne*-detector, resulting in an increase of the Ne*-signal. This is actually observed experimentally. From the positions of the Zeeman-lines of figs. 8 and 9, we have performed a least-squares analysis of the Land6 factors of the three levels involved. The results are in agreement with the theoretical values of table 1. The magnetic field value, which corresponds with these peak positions, is B= 222 + 1 G. The error bar results from the uncertainty in the frequency step 0.484 f 0.002 MHz/V. A very good agreement is observed with the experimental value 8~224 G, which is obtained with a Hall-probe. According to eq. ( 11) the relative spacing between the Zeeman-lines is 5 1.7 MHz, which is a factor 2 smaller compared with the transition of eq. ( 13 ) . Therefore, we have to be careful because neighbouring substates may be pumped as well at large laser intensities, due to power-broadening of the line widths. We can conclude that collision experiments can

J.P.J. Driessen et al. /Purestate Ne*, New preparation

458

thus be performed with pure Ne** [a,, IJ= 3, M = ? 3)B]-states. By rotating the magnetic field B in the collision-plane with respect to the relative velocity g, it is possible to study the polarization effect of Ne** [ cy9,J= 3, M ] -Ar collisions.

4. Polarization effects in the Ne*[3P&4r system 4.1. Experimental signals At the metastable-atom detector downstream of the scattering center, we measure the time-of-flight spectrum S” ( t, 1Ld) using a flight path Ld from chopper to detector. In each time-channel n centered at flighttime tn=Ld/v,,, with v,, the velocity of the atom, the number of counts for each chopper period is given by S”(&l IL) =~m~(0)S2dJYt, lL’)r,‘l =~“~‘“(tn

IL&,” 9

(15)

with qrnthe efficiency for metastable-atom detection. The flux krn( t, )Ld) of metastable atoms arriving at the detector with flighttime t, is determined by the center line intensity Z(O), the solid angle sl, of the primary beam seen by the detector, the duration of one time channel T,,, and the flighttime distribution From the time-of-flight spectrum F(t”l&i). S” (t, ILd) we can determine by deconvolution the velocity distribution, which is then convoluted once more to determine the time-of-flight spectrum S” ( tk) of metastable atoms arriving at the scattering center. This procedure of spectrum transformation is described in detail by van Vliembergen et al. [ 26 1. Collisions with secondary beam atoms at the scattering center will produce Penning electrons with a kinetic energy e. z 0.9 eV. The number of counts from the channeltron detector Selac(tk) that is registered in time channel k for each chopper-period is equal to

Selec(tk) =qe%&, (dgk/vk)&“(tk) X [‘f ‘Q(sd + “f oQ(h’d + ‘f ‘Q(&) 1 ,

(16)

with qeiec the efficiency for electron detection and (n&k/&) the effective density-length product ofthe secondary beam as seen by the primary Ne*-beam. The superscripts 2, 0 and r refer to the metastable states “Ne* [ ‘PZ], 2oNe*[ 3Po] and the 22Ne*-isotope, respectively. The relative populations of these

different states are denoted by if and their ionization cross sections are given by ‘Q. The ionization cross section 2Q( E I M,) can now be determined according to eq. (3). Using the natural isotope abundances ( 20Ne: 22Ne= 9 1: 9 ) and assuming a statistical distribution over the metastable states we find ‘fzO.76, OfxO.15, ‘-JzO.O~~~~‘Q=(OQ+~~Q)/~. The electron detection efficiency flee is determined by the total transparency T, the solid angle acceptance and the quantum efftciency rp” of the channeltron detector. Based on the calculated transparency T~0.947, the solid angle acceptance efficiency fl=2n/4tr=OSO and the specified quantum efficiency tp’ = 0.60, we expect to have rf”” = 0.26. By performing collision experiments without state selection for the He*, Ne*-Ar systems, with well-known ionization cross sections [ 14,27 1, we were able to determine the ratio p/?‘@ec of eq. (3). The metastableatom detection efficiency #“co.54 has been determined by scaling [ 131 to the ion detection efficiency $‘“, for which we assume the value $‘“=0.60. The resulting value for the electron detection efficiency is rFlet= 0.13. Because we know that r,@”G 1 and p Q 1, this implies an upper limit yFlec&0.22. The discrepancy of this upper limit with the calculated value 9=lec= 0.26 is unexplained as yet. 4.2. Laser-modulation technique In separate experimental runs we deplete the different magnetic substates IJ, Mi)B of the Ne*-atom with the laser tuned at the transition-frequency of eq. (12). The time-of-flight spectrum &Sm(tklM’) of these substates can be determined through the difference of the metastable-atom signals with laser switched on and off, ~m(tkI~i)=S~(tk)-S~n(fkl~i)

(17)

*

In a similar way we obtain the time-of-flight spectrum AS”‘”( tk IMi ) of the electrons, which result from the depleted Ne* [ IJ= 2, M’ ) B]-states. ~e’ec(tkIMi)=S~~(fk)-S~~(tklMi)

e

(18)

The ionization cross section ‘Q(EIMi) can now be determined according to eq. ( 3 ) , 2Q(EIbfi)=(d&/Vk)-’

~~~t~l~~

L

&.

(19)

J.P.J. Driessenet al. /Purestate Ne*, Ne**preparation

459

This CTOSSsection ‘Q(EIMi) refers to a pure magnetic substate with respect to the magnetic field ( 1J= 2, A4i)B)- However, we are mainly interested in the polarized-atom cross section 2QlMr(E) for an asymptotic pure substate with respect to the relative velocity g. The connection between these cross sections is given by ‘Q(EIMi)=

,E,

I4@~(B)l”

2Q’M’(E) 3

(20)

with /I the angle between the magnetic field Band the relative velocity g. The Wigner d-function d$$ (/I) describes the pure 1J= 2, Mi )rstate as a distribution over IJ= 2, M)6states. In fig. 10 we show the rotated lM1 -population of the I.I= 2, + M)dstates as a function of the angle jl. For an angle /3=0 we measure the polarized-atom cross section ‘Q I”I (E) directly. Experimentally, this angle cannot be reached for all collision energies as is shown in fig. 6. At thermal energies the detector is positioned at the lab-angle &,= 35 ‘. The corresponding /I-range 0” d /?< 15 o results in IMI -distributions which represent nearly pure magnetic substates. In the superthermal energy range the detector is placed at BB=108”,giving85”~/3695”.Thisleadstoasetof IMI -distributions from which the polarized-atom cross sections 2Q ~4’(E) can be solved accurately according to eq. ( 20). The size of the laser beam at the scattering center is 3.6 mm full width at 1/e2 of maximum intensity. The Ne* [ 3P2, A4] -substates are depleted before they reach the interaction region, because the laser beam is positioned 1.5 mm upstream of the scattering center. The laser beam is positioned at the interaction region by optimizing the countrate for the “fast” electrons, as discussed in section 5. The laser intensity in the collision experiment is I= 1.O mW.

60 p (degrees)

to-.,

I

\

-

I

I

I

I

b_

Mi= 1

\

\ \

30

0

60

90

p Idegrees) 1.0

_

‘%.

,

‘\

I

I

C_

Mi-2 ‘\

‘\ IMI-2’1.

z 5

I

I

‘.\

\

1. \

4.3. ExpPrimental results The magnetic substates Ne* [ 3P2, Mi] are depleted with the laser tuned at the Zeeman-lines, denoted as 7, 10 and 12 according to fig. 7. The magnetic field B is directed at 19,= 35 o in the thermal energy range and at e p 108” at superthermal energies. The resulting ionization cross sections 2Q( E I M) can thus be solved in terms of the polarized-atom cross section 2Q I”’ (E)

0

30

60

90

p (degrees1 Fig. IO. The 1Ml -population of the Ne*[ 3P2, IJ, f M>,]-states as a function of the angle B= L (B, g) for the three pumped Ne*[3P2, IJ, Mi>s]-states.The )MJdistribution is given by the squared Wigner d-functions Itic&( 8) I 2.

J.P.J. Driessen et al. /Purestate Ne*, Ne** preparation

460

Table 3 The cross section results for the Ne* [ “PO,‘P2] -Ar system. For comparison the results of Verheijen et al. [ 141 have been included together with the experimental polarization effect of Bregel et al. [ 271. The number in parentheses is the error in the last digits given E

2Qo/ZQ

‘Q’/‘Q

‘Q212Q

‘Q (A21

(eV

‘) Bregeletal.

this work

ref. [ 141

0.075 0.095 0.125 0.180

1.13(3) 1.19(3) 1.27(2) 1.24(3)

1.14(3) 1.17(3) 1.02(2) 1.08(3)

0.79(2) 0.73(3) 0.85( 1) 0.80(3)

19.2(2.4) 18.5( 1.5) 18.2(1.4) 20.5(2.1)

16.9 17.3 18.1 19.7

1.oo 2.45

1.14(5) 1.05(6)

0.96(3) 0.85(4)

0.97(3) I.l2(3)

16.1(1.0) 16.9(0.7)

22.8 17.7

0.050 l’ 0.100”

1.13(3) 1.07(4)

1.13(8) 1.07(8)

0.81(3) 0.89(4)

[27].

with high accuracy. In table 3 we present the cross section results. The average cross section ‘Q(E) is given together with the polarization effect 5e(E) = 2Q’M’(E)/2Q(E). For comparison we have included the cross section results of Verheijen et al. [ 141 and the polarization effect of Bregel et al. [ 28 ] at collision energies of E= 50 meV and E= 100 meV. We observe a significant polarization effect with the largest cross section for the Ne* [ 3P2, 1J, Mi = 0, 1 ),I states at thermal energies, while at superthermal energies the Ne* [ ‘P2, (J, Mi = 2 ),I -Ar system ionizes most effectively. At thermal energies the polarization effect confirms the results of Bregel et al. [ 28 1. Our absolute cross section values are less reliable than the results of Verheijen et al. [ 141, because we have a lower statistical accuracy. The reason for this is threefold. Firstly, we modulate only a 12% of the metastable atoms in our setup (table 2), whereas Verheijen modulates x 75% of the metastable atoms. Secondly, we have a small electron detection efficiency @IK: = 0.13 which results in typical electron countrates of Selec= 400 Hz in contrast to the ion detection efficiency of Verheijen [ 13,141, d,, = 0.60, giving typical ion countrates of Sian= 2500 Hz. Thirdly, the electron detector has a large &dependent backgroundcountrate (TMS: 50- 100 Hz, HCA: 300-600 Hz), while the ion detector has a zero background-countrate.

5. Polarization effects in the Ne**[a%i#Ar

system

5.1. Calibration of the electron detector If the laser is tuned to excite the two-level system in the scattering center, eq. ( 14)) Penning electrons are emitted which differ approximately 1.8 eV in kinetic ehergy (eq. ( 1) ). By applying a blocking voltage Uti, at the selection grids, we can suppress the electron countrate from the metastable Ne*-atoms as discussed in section 2.4. In fig. 11 we show the total electron countrate SC’CC as a function of the blocking voltage Uti, for the situation with laser switched on and off. At a selection voltage of U,, = -3.5 V all “slow” electrons (e * 0.9 eV) are suppressed, while the “fast” electrons (ea2.7 eV) are stopped at a voltage of Ufid= -6.0 V. Although the applied blocking voltage LItid is not proportional to electron energy c, the energy distribution of the emitted electrons can be approximated by the derivative p== ( U) =

-&-sy U)

)

(21)

which is also given in fig. 11. We note that the separation of the two collision processes of eq. ( 1), which is the main aim of the new detection technique, is very well practicable. Typical countrates for the “fast” electrons are Seiee=400 Hz in the thermal energy range and SC’&=200 Hz in the superthermal energy range. These signals are corrected for the &dependent back-

J.P.J. Driessen et al. /Pure state Ne*, Ne**preparation

461

rect analysis to determine this angle-dependence of dl=(es). We investigate the &dependence of @‘“(&) by measuring the electron signal Se’ccfor a collision system with a negligible polarization effect. For Ne** [ a9 ] -Ar collisions at superthermal energies (0.5 GE (eV) G 5 ) the polarization effect is indeed negligible as is shown by Driessen et al. [ 13 1. The electron signal Pet, however, shows a clear &-dependence as is demonstrated in fig. 12. The solid line through the data represents the expected electron signal, based on previous measurements of Driessen et al. [ 13 1. The dashed line gives a least-squares curve representing the &,-dependence according to rl”ec(es)=rle’==(90~)F(e~), F(e,)= 0.11 0

I I

I 2 blocking

/ 3

ui

4 voltage U IVolt

I 5

I 6

Fig. II. The total electron countrate .Y’= as a function of the blocking voltage V,,+,for the situations with laser on and off. The derivative P*=(d/dU)Sc, which is approximately proportional to the energy distribution of the emitted electrons, which is also presented.

ground-countrates (TMS: 50- 100 Hz, HCA: 300-600 Hz ) . We thus obtain less accurate absolute cross section values in comparison with the ion-detection technique used previously [ 13- 15 1, with typical ion countrates Sian=2500 Hz and a zero backgroundcountrate. The difference cross section determined with the ion detector (eq. (2) ), results in a strong interdependence of the polarization effects of both upper and lower level of the neon two-level system [ 13 1. Our polarization effect, however, is more accurate because the “fast” electrons are measured separately. Because in the two-level system only one pure magnetic substate 1J= 3, Mk= + 3),, can be excited with a significant upper level population, the electron signal has to be measured as a function of the detector-orientation in the collision plane in order to obtain the four polarized-atom cross sections 3Q’Mt(E) (section 5.3). The electron detection efflciency vlec, however, may depend on the lab-angle 0, characterizing the orientation of the rotating detector (0, = L (B, vI ); fig. 6). It is thus essential for a cor-

l.oo+ 1.24x io-3 (e,-900)

- 6.1 x 10-5 (e,-900)*,

(22)

with qelec( 90” ) = 0.13 (section 4.1) . Therefore, we scale the electron signal with this function F( 0,) to correct for the angle-dependent electron-detection efficiency v’m ( e,) . 5.2. Upperlevelpopulation The true neon two-level system in a magnetic field B is given by eq. (14), with the 15=3, Mk= f 3)B state as the upper level. Because the upper level is populated over the whole interaction region, a signif-

I

0

30

1

I

60

90

I

120

I

150

180

egldegreesl

Fig. 12. The relative detection efficiency q”(&)/p(90” ), as measured by the electron countrate S& for the Ne**[c+]-Ar system in the supertheenergy range as a function of the labangle ~9,= L (4 n,) (see fig. 6). The expected behaviour according to Driessen et al. [ 131 is indicated by the solid line. The dashed line represents a least-squares curve through the measured data.

J. P.J. Driessen et al. /Pure slate Ne? Ne+* preparation

462

icant electron countrate in the ionization experiment for the excited upper state is possible. In order to obtain absolute values of the cross sections, the relative upper level population VP*must be known. In a true two-level system this population parameter is a function of the laser intensity Z, as given by [ 291

1 z/z, rpp*_ -ziqiy

(23)

with Z,the so-called saturated laser intensity at tp”’= 4. As a result of the statistical distribution over the magnetic substates of the lower level only ?j‘f= 15% of the metastable neon atoms can be excited. With the laser beam switched on the rate of arrival of atoms in the short-lived upper level is equal to

=j 2&Vrn( fk) /rjrn7&

)

(24)

with S” ( tk) the flighttime-resolved countrate of the detected Ne* [‘PO, ‘P2 ]-atoms at the metastable-atom detector. To obtain absolute values of the cross section, we have to determine the upper level population tp”’ in eq. (24). Therefore, we have measured the countrate Sclec( zkI p) of the “fast” electrons as a function of the laser intensity Z for the Ne**-H2 system. The laser beam is positioned at the interaction center by optimizing this electron countrate. The Gaussian laser beam profile has a full width waist size of 3.6 mm at 1/e2 of the maximum intensity. Both the ionization cross section and the density-length product (nl) are much larger for Ne**-H2 collisions, resulting in much larger electron countrates. The experimental results are given in fig. 13. We do not observe the behaviour of eq. ( 23 ) . Instead we notice a steady increase of the electron signal with increasing laser intensity, with no saturation effect according to the relation S&C(Z) _

IO.4594

,

(25)

which has been determined in a least-squares analysis. This curve has been indicated in fig. 13 as well. The non-saturating behaviour is probably due to the fact that at higher laser intensities the linewidths are broadened so much that neighbouring substates are excited. The most likely candidates are the Ne* [ 1.I= 2, M= + 1 )B]-states, which are excited in the transitions 4’ and 12’ in figs. 7 and 9. At a laser

0.1

0.01

1 laser

10

xx,

power (mWI

Fig. 13. The electron countrate Se’” for the Ne** [ (us]-H2 system as a function of the laser intensity I. No saturation according to eq. (23 ) is observed. Instead the electron signal increases continuously according to the relation Se’“-Io~“59’, which is determined in a least-squares analysis and which has been indicated by the solid line.

power I= 1.0 mW the estimated power-broadened linewidth is 50 MHz, where the measured linewidth of the transitions 6 and 7 have been used as a reference (table 2 ) . This value should be compared to the spacing AV= 5 1.7 MHz between the Zeeman-lines. In the radiative decay these states can end up in the real two-level system and thus contribute to the countrate of the “fast” electrons. For I= 10 mW this effect is even more pronounced, due to the increase of the linewidth proportional to I’/‘. The absolute value of the population parameter tpp’ is therefore still undeTable 4 The cross section results for the Ne** [ag]-Ar system. The average cross section ‘Q(E) has been determined by Driessen et al. [ 131 and has been used to calculate the upper level population parameter rpp’according to eq. (27 ). The polarization effect is characterized by W”*’= ,Q”*‘/ 3Qand Wrs3= 3Q2*3/‘Q. The number in parentheses is the error in the last digit given 90.1

gp.3

3Q”

0.065 0.090 0.115 0.165

1.30(4) 1.28( 1) 1.31(3) 1.28(2)

0.78(3) 0.79(l) 0.77(3) 0.79(2)

27.3 25.0 23.4 22.1

0.62 0.53 0.51 0.49

1.20 2.75

1.03(7) 0.98(S)

0.98(S) 1.02(S)

20.1 15.6

0.21 0.21

E (ev)

a1 Driessen et al. [ 131.

(AZ)

rp”

J.P.J. Driessenet al. /Purestate Ne? Ne**preparation

463

termined. Because absolute cross section values for the Ne** [ ag] -Ar system are available (Driessen et al. [ 13 ] ), we can determine the upper level population by scaling our cross sections. The results will be given in table 4. 5.3. Measuring routine By suppressing the electrons resulting from the metastable Ne*-atoms, we measure an electron countrate resulting from the excited Ne** [ cy9, ]J= 3, M = + 3)8 J-state. In collisions of Ne*(*)-atoms with residual background atoms/molecules, extra fast electrons may be produced. To correct for these extra electrons we apply the laser-modulation technique in order to obtain the time-of-flight spectrum A 3Se’ec( tk I /I) of the electrons which result from the excited 1J= 3, M= + 3 ) satoms colliding with Ar

with /I the angle between the magnetic field B and the relative velocity g and flec(fl) the angle-dependent detection efficiency as given in section 5.1. The ionization cross section 3Q(E]fi) can now be determined through

(27) This cross section 3Q(E] 8) refers to a pure magnetic substate with respect to the magnetic field IJ= 3, M= + 3 >=. Our aim is to determine the polarized-atom cross sections 3Q’M’(E) for an asymptotic pure substate with respect to the relative velocity IJ= 3, M)r These cross sections are related through

‘Q(EIS)=

,$_,ld:~~(~)l'~Q"""(E).

(28)

From a least-squares analysis with eq. (28) we can thus determine the cross sections 3Q IMH (E). In fig. 14 we show the squared Wigner d-function I d$G3(~3)I 2, which appears in eq. (28 ). We observe that the ]M] ~0, l-states are almost equally populated for all angles fi. Furthermore, we note that only

p (degrees)

Fig. 14. The 1MI -population of the Ne** [ ap, 1J, k M),]-states as a function of the angle /3= L (B, 8) for the excited Ne**[cug,J, Mi= +3>,]-states. The [MI-distribution is given by the squared Wigner d-functions I&$( 8) I‘.

a limited prange can be chosen, corresponding with the B-range of fig. 6. Thus it is very difficult to discern between the separate )Q MI (E) cross sections. 5.4. Experimental results The upper level of the two-level system Ne*[3P2,Mi=k2]*Ne**[09,Mi=?3] isexcited with the laser tuned at the Zeeman-line, denoted 11’ in figs. 7 and 9. The magnetic field B is rotated in the collision plane between the lab-angles 3 5 o < & s 145 ‘. The corresponding &range depends on the collision energy E. The cross sections ‘Q( El /?), which are measured for these Bangles, can be solved in terms of the polarized-atom cross sections 3Q’M’(E). Because the interdependence of these cross sections is quite large we are forced to determine the average cross sections 3Q0*‘(E)=f[3Qo(E)+2

‘Q’(E)],

3Q2*3(E)=;[3Q2(E)+3Q3(E)].

(29)

In table 4 we present the cross section results. The polarization effects WOJ(E) = 3Qo*’(E) /3Q( E) and 9 2,3(E) = 3Q2~3(E) /3Q( E) are presented. The average cross section ‘Q(E) has been determined by Driessen et al. [ 131 and is also given in the table. It

J.P.J. Driessen et al. /Pure state Ne*, Ne** preparation

464

is used to calculate the population parameter tp”’ which is included in the table as well. We observe a pronounced polarization effect with a strong energydependence. In order to obtain insight in the collision dynamics and the optical potentials, we have performed semiclassical calculations for the Ne**-Ar system. A detailed description of the semiclassical model is given by Driessen et al. [ 131 and in a second paper [ 301 the calculated autoionization widths are presented, which are necessary in the calculation. In table 5 we compare our experimental results with the calculated data. A good agreement is achieved. The polarization effect has been determined previously by Driessen et al. [ 131, who used the ion-detection technique. The difference cross section is determined with the ion detector, resulting in a strong interdependence of the polarization effects of both upper and lower level of the neon two-level system [ 13 1. Thus a polarization effect must be assumed for the lower level in order to determine the polarized-atom cross sections 3Q’“’ of the upper level. The difference cross sections have been analysed in two ways [ 131: first, the polarization effect in ‘Q(E) is neglected and, second, an energy-independent polarization effect 'QO*' / ‘Q* = 4/3 is assumed. The polarization effect So,’ (E) and L%‘**~(E)obtained in this manner is also included in table 5. In the thermal energy range our polarization effect is in good agreement with the second analysis, Table 5 Comparison of the experimental polarization effect with semiclassical model calculations [ 3 11. We have also included previous results of Driessen et al. [ 131, obtained with iondetection technique, who analyzed the difference cross section with two assumptions for the polarization effect of the lower level. The number in parentheses is the error in the last digit given E (ev)

3Qo~‘(E)/3Q2”(E) experiment

0.075 0.125 0.200 1.000 2.500

semi

a)

b)

this work

1.40(6) l.52(6) 1.27(5) 1.15(4) l.OO(3)

1.59(6) 1.77(7) 1.52(5) 1.35(4) 1.24(4)

1.66(8) 1.70(6) l.62(3) 1.05(11) 0.96( 1 I )

1.69 1.74 1.76 1.28 0.91

‘) Driessen et al. [ 131, neglecting polarization effect in *QI”‘. b, Driessen et al. [ 131, assuming *Q”~‘/2Q2=4/3.

while in the superthermal energy range our results confirm a negligible polarization effect of the lower level. This general picture of the energy dependence of the polarization effect *Q”~‘/*Q2 is in good agreement with our results (section 4.2, table 3).

6. Discussion and conclusion In this paper we have presented the first results obtained with a new electron detector. The energy-dependent polarization effect in the ionization cross section can be measured accurately. The accuracy of the absolute cross section values, however, can be optimized by suppressing the large background countrates. Elastic scattering of Ne*-atoms resulting in secondary electron emission on various surfaces in the detector contributes to the background signal. These disturbing processes have to be investigated in the future. In the absence of atomic beams the countrate of the detector is still too large (50-200 Hz), indicating that the pulse counting electronics can be improved. The interdependence of the polarized-atom cross sections is completely removed if the magnetic field B is aligned parallel to the relative velocity g. The Newton diagram of fig. 6 shows that perfect alignment is not possible for all collision energies E. We can improve the Newton diagram by increasing the velocity v2 of the Ar-atoms. This can be achieved by seeding with helium. Because the He target atoms are not ionized in collisions with the Ne*(*‘-atoms, the electron signal is not disturbed. For the Ne** [ oP]-H2 system we have measured the polarized-atom cross sections in the thermal energy range, for which large signals are obtained because the ionization cross sections are very large [ 3 1] and the density-length product of the secondary beam is very high. For most molecular targets a large cross section is observed and large signals can be expected. A significant polarization effect is observed: W”~‘(E)=1.10f0.03 and 5P2~3(E)=0.90+0.03, which is larger than found in previous measurements [ 3 11. The energy dependence of the average ionization cross section shows a strong increase with decreasing energy E. This is in good agreement with the orbiting collision model [ 3 1 1, which predicts

J.P.J. Driessen et al. /Pure state Ne? Ne**preparation

Q- 5.94(C,JE)“’

,

(30)

with C, the van der Waals coefficient. Because the ionization processes with shortlived laser excited Ne**-atoms can be measured separately without disturbing electron signals originating from the metastable Ne*-atoms, we will investigate the possibility to study the ionizing collisions involving shortlived Ne** [ ak # a9] -atoms. The expected electron countrate is very small due to the short lifetime of the Ne**-states (rx20 ns, vz 1000 m s-i, I,= v5x 20 pm). The electron signal can be enlarged by increasing the beam intensities. A free supersonic expansion as a secondary beam results in much larger density-length products (nl), as is described by Manders et al. [ 10 1. Furthermore, the primary beam flux through the scattering center can be made more intense by transverse cooling of the Ne*-atoms. In the future these possibilities will be investigated.

Acknowledgement

This work is supported by the Foundation for Fundamental Research on Matter (FOM).

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